mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 15:01:08 +00:00
760d9bedc1
* Feat: Added Fast inverse square root * Fix: Added typehint * Fix: Added doctests that break the code, changed var name * updating DIRECTORY.md * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fix: fixed length of docstring * Update fast_inverse_sqrt.py --------- Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
55 lines
1.7 KiB
Python
55 lines
1.7 KiB
Python
"""
|
|
Fast inverse square root (1/sqrt(x)) using the Quake III algorithm.
|
|
Reference: https://en.wikipedia.org/wiki/Fast_inverse_square_root
|
|
Accuracy: https://en.wikipedia.org/wiki/Fast_inverse_square_root#Accuracy
|
|
"""
|
|
|
|
import struct
|
|
|
|
|
|
def fast_inverse_sqrt(number: float) -> float:
|
|
"""
|
|
Compute the fast inverse square root of a floating-point number using the famous
|
|
Quake III algorithm.
|
|
|
|
:param float number: Input number for which to calculate the inverse square root.
|
|
:return float: The fast inverse square root of the input number.
|
|
|
|
Example:
|
|
>>> fast_inverse_sqrt(10)
|
|
0.3156857923527257
|
|
>>> fast_inverse_sqrt(4)
|
|
0.49915357479239103
|
|
>>> fast_inverse_sqrt(4.1)
|
|
0.4932849504615651
|
|
>>> fast_inverse_sqrt(0)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: Input must be a positive number.
|
|
>>> fast_inverse_sqrt(-1)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: Input must be a positive number.
|
|
>>> from math import isclose, sqrt
|
|
>>> all(isclose(fast_inverse_sqrt(i), 1 / sqrt(i), rel_tol=0.00132)
|
|
... for i in range(50, 60))
|
|
True
|
|
"""
|
|
if number <= 0:
|
|
raise ValueError("Input must be a positive number.")
|
|
i = struct.unpack(">i", struct.pack(">f", number))[0]
|
|
i = 0x5F3759DF - (i >> 1)
|
|
y = struct.unpack(">f", struct.pack(">i", i))[0]
|
|
return y * (1.5 - 0.5 * number * y * y)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
from doctest import testmod
|
|
|
|
testmod()
|
|
# https://en.wikipedia.org/wiki/Fast_inverse_square_root#Accuracy
|
|
from math import sqrt
|
|
|
|
for i in range(5, 101, 5):
|
|
print(f"{i:>3}: {(1 / sqrt(i)) - fast_inverse_sqrt(i):.5f}")
|